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Rapport Année : 2012

On matrix exponential approximations of the infimum of a spectrally negative Levy process

Andras Horvath
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M.R. Pistorius
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Résumé

We recall four open problems concerning constructing high-order matrix-exponential approximations for the infimum of a spectrally negative Levy process (with applications to first-passage/ruin probabilities, the waiting time distribution in the M/G/1 queue, pricing of barrier options, etc). On the way, we provide a new approximation, for the perturbed Cramer-Lundberg model, and recall a remarkable family of (not minimal order) approximations of Johnson and Taaffe , which fit an arbitrarily high number of moments, greatly generalizing the currently used approximations of Renyi, De Vylder and Whitt-Ramsay. Obtaining such approximations which fit the Laplace transform at infinity as well would be quite useful.
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Dates et versions

hal-00739232 , version 1 (09-10-2012)

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Florin Avram, Andras Horvath, M.R. Pistorius. On matrix exponential approximations of the infimum of a spectrally negative Levy process. 2012. ⟨hal-00739232⟩
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